State laws and insurance guidelines differ but normally if your car has been declared a total loss the check will be made out directly to the insured and the lien holder. If the settlement check for the actual cash value (ACV) of the car is more than what is owed on the vehicle you should get money back out from the settlement amount once the loan has been paid in full.
If you are getting repairs made to the vehicle then the check may be made out to both the insured (policyholder) and repair shop or insured and lien holder or even possibly be made out directly to the repair shop. If you were to receive a check that was made out to you and the finance company then you would normally need to endorse the check and send it to the finance company if they are to pay for the repairs. Once they receive an invoice from the repair shop for the repairs, they will also endorse the check and then forward that check to the repair shop.
When you have a lien holder, and thus are not technically yet the full owner of your car, settlement checks or checks for repairs or a total loss are normally made out to both the policyholder and the financial institute, lender, which holds the title to your car. The lending institute's name is on the check because your car is collateral for your loan. The bank (or whoever is financing the car) has an interest in making sure the money is used to repair the car and not for anything else. In case of a total loss the lender makes sure the money is used to pay on the loan.
An insurance company will typically notify the lien holder if they are going to write a check to make the insurable interest (vehicle) whole. Since both the lien holder and the insured driver have an interest in the value of the vehicle, normally they are both notified about physical damage claim reimbursements of any amount.
If the financed car was a total loss and you are receiving a settlement check then usually the check from the insurance company will have your name and the name of the finance company on the check. You would then endorse the check and turn it over to the finance company. The finance company will pay off the loan and if there is money left over they should refund the difference to you. If the pay off on the loan is greater than the check from the insurance company then the finance company would keep the entire check amount and you will still owe the finance company the difference. If you purchased gap insurance the financier would also receive the check, or the check again would be made out to both you and the lien holder again for you to endorse and sign over to them.
So to protect the lien holder's interest in the vehicle, many insurance companies will cut the settlement or repair checks in both your name and an additional payee which would be the lien holder (finance company). If your vehicle has been totaled out or having repairs made due to an accident and you want to know how the check will be made out, speak to the insurance adjuster working your claim.